Stable motions of high energy particles interacting via a repelling potential
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916056625315840 |
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| author | Rom-Kedar, V. Turaev, D. |
| author_facet | Rom-Kedar, V. Turaev, D. |
| contents | The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all sufficiently large energies. Specifically, choreographic solutions, for which all particles follow approximately the same path close to an elliptic periodic orbit of the single-particle system, are proved to be KAM stable in the high energy limit. Finally, it is proved that the motion of N repelling particles in a rectangular box is non-ergodic at high energies for a generic choice of interacting potential: there exists a KAM-stable periodic motion by which the particles move fast only in one direction, each on its own path, yet in synchrony with all the other parallel moving particles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_14993 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stable motions of high energy particles interacting via a repelling potential Rom-Kedar, V. Turaev, D. Dynamical Systems Mathematical Physics Chaotic Dynamics Classical Physics The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all sufficiently large energies. Specifically, choreographic solutions, for which all particles follow approximately the same path close to an elliptic periodic orbit of the single-particle system, are proved to be KAM stable in the high energy limit. Finally, it is proved that the motion of N repelling particles in a rectangular box is non-ergodic at high energies for a generic choice of interacting potential: there exists a KAM-stable periodic motion by which the particles move fast only in one direction, each on its own path, yet in synchrony with all the other parallel moving particles. |
| title | Stable motions of high energy particles interacting via a repelling potential |
| topic | Dynamical Systems Mathematical Physics Chaotic Dynamics Classical Physics |
| url | https://arxiv.org/abs/2208.14993 |